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Lattice animal is a set of connected sites on a lattice. Lattice animals on a square lattice are especially popular subject of study and are also known as polyominoes. Polyomino is usually represented as a set of sidewise connected squares. Polyomino with $n$ squares is called $n$-polyomino.
In this problem you are to find a number of distinct free $n$-polyominoes that fit into rectangle $w \times h$. Free polyominoes can be rotated and flipped over, so that their rotations and mirror images are considered to be the same.
For example, there are 5 different pentominoes (5-polyominoes) that fit into $2 \times 4$ rectangle and 3 different octominoes (8-polyominoes) that fit into $3 \times 3$ rectangle.
The input file consists of a single line with 3 integer numbers $n$, $w$, and $h$ ($1 \le n \le 10$, $1 \le w, h \le n$).
Write to the output file a single integer number --- the number of distinct free $n$-polyominoes that fit into rectangle $w \times h$.
5 1 4
5 2 4
5 3 4
5 5 5
8 3 3